[Une solution analytique du système de Saint-Venant couplé à lʼéquation dʼExner]
Cette Note présente une solution analytique pour le système modélisant le transport de sédiments par le charriage. Cette solution est valable pour une grande famille de lois sédimentaires comme le modèle de Grass ainsi que celui de Meyer-Peter et Müller. Ce résultat est utile pour la validation des schémas numériques.
In this Note, an exact smooth solution for the equations modeling the bedload transport of sediment in shallow water is presented. This solution is valid for a large family of sedimentation laws which are widely used in erosion modeling such as the Grass model or those of Meyer-Peter and Müller. One of the main interests of this solution is the derivation of numerical benchmarks to valid the approximation methods.
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@article{CRMATH_2012__350_3-4_183_0,
author = {Christophe Berthon and St\'ephane Cordier and Olivier Delestre and Minh Hoang Le},
title = {An analytical solution of the shallow water system coupled to the {Exner} equation},
journal = {Comptes Rendus. Math\'ematique},
pages = {183--186},
publisher = {Elsevier},
volume = {350},
number = {3-4},
year = {2012},
doi = {10.1016/j.crma.2012.01.007},
language = {en},
}
TY - JOUR AU - Christophe Berthon AU - Stéphane Cordier AU - Olivier Delestre AU - Minh Hoang Le TI - An analytical solution of the shallow water system coupled to the Exner equation JO - Comptes Rendus. Mathématique PY - 2012 SP - 183 EP - 186 VL - 350 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2012.01.007 LA - en ID - CRMATH_2012__350_3-4_183_0 ER -
%0 Journal Article %A Christophe Berthon %A Stéphane Cordier %A Olivier Delestre %A Minh Hoang Le %T An analytical solution of the shallow water system coupled to the Exner equation %J Comptes Rendus. Mathématique %D 2012 %P 183-186 %V 350 %N 3-4 %I Elsevier %R 10.1016/j.crma.2012.01.007 %G en %F CRMATH_2012__350_3-4_183_0
Christophe Berthon; Stéphane Cordier; Olivier Delestre; Minh Hoang Le. An analytical solution of the shallow water system coupled to the Exner equation. Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 183-186. doi : 10.1016/j.crma.2012.01.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.01.007/
[1] E. Audusse, C. Chalons, O. Delestre, N. Goutal, M. Jodeau, J. Sainte-Marie, B. Spinewine, Sediment transport modelling: Three layer models and relaxation schemes, CEMRACS Proceedings, 2011, submitted for publication.
[2] Sediment transport models in shallow water equations and numerical approach by high order finite volume methods, Computers & Fluids, Volume 37 (March 2008) no. 3, pp. 299-316
[3] Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help, Advances in Water Resources, Volume 34 (2011) no. 8, pp. 980-989
[4] O. Delestre, C. Lucas, P.-A. Ksinant, F. Darboux, C. Laguerre, T.N.T. Vo, F. James, S. Cordier, SWASHES: a library of shallow water analytic solutions for hydraulic and environmental studies, submitted for publication, . | arXiv
[5] Über die wechselwirkung zwischen wasser und geschiebe in flüssen, Sitzungsber., Akad. Wissenschaften pt. IIa, Volume 134 (1925)
[6] A.J. Grass, Sediment transport by waves and currents, SERC London Cent. Mar. Technol. Report No. FL29, 1981.
[7] J. Hudson, Numerical technics for morphodynamic modelling, PhD thesis, University of Whiteknights, 2001.
[8] E. Meyer-Peter, R. Müller, Formulas for bed-load transport, in: 2nd meeting IAHSR, Stockholm, Sweden, 1948, pp. 1–26.
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A limitation of the hydrostatic reconstruction technique for Shallow Water equations
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